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A138255 Smallest positive integer m such that n divides [2^m/m] (=A000799(m)).

%I A138255 #19 Aug 24 2023 10:22:55
%S A138255 1,1,5,4,6,5,9,8,7,6,12,15,14,9,13,8,10,7,21,28,13,24,48,15,22,14,19,
%T A138255 9,30,13,11,8,31,10,13,21,38,21,14,39,22,13,29,63,13,67,135,65,43,22,
%U A138255 10,15,35,19,24,9,21,30,120,28,62,11,13,16,14,31,69,20,67,13,145,21,19,38
%N A138255 Smallest positive integer m such that n divides [2^m/m] (=A000799(m)).
%C A138255 This sequence is well-defined.
%H A138255 Robert Israel, <a href="/A138255/b138255.txt">Table of n, a(n) for n = 1..10000</a>
%H A138255 Romanian Master in Mathematics Contest, <a href="https://artofproblemsolving.com/community/c6h187665">Problem 3</a>, Bucharest, 2007.
%p A138255 f:= proc(n) local m;
%p A138255      for m from 1 do if floor(2^m/m) mod n = 0 then return m fi od
%p A138255 end proc:
%p A138255 map(f, [$1..100]); # _Robert Israel_, Jun 07 2018
%t A138255 a[n_] := For[m = 1, True, m++, If[Divisible[Floor[2^m/m], n], Return[m]]];
%t A138255 Array[a, 100] (* _Jean-François Alcover_, Mar 22 2019 *)
%o A138255 (Python)
%o A138255 from itertools import count
%o A138255 def A138255(n): return next(m for m in count(1) if not (1<<m)//m%n) # _Chai Wah Wu_, Aug 24 2023
%Y A138255 Cf. A000799, A138256, A138257, A138258, A138259, A138260, A138261, A138262, A138263.
%K A138255 nonn
%O A138255 1,3
%A A138255 _Max Alekseyev_, Mar 09 2008